数学与计算机科学 |
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END随机变量序列移动平均过程的极限性质 |
宋明珠, 邵静, 刘彩云 |
铜陵学院 数学与计算机学院,安徽 铜陵 244000 |
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Limiting properties of moving average processes for END random variable sequence |
SONG Mingzhu, SHAO Jing, LIU Caiyun |
Institute of Mathematics and Computing,Tongling University, Tongling 244000, Anhui Province,China |
1 EBRAHIMI N, GHOSH M. Multivariate negative dependence[J]. Communications in Statistics A, 1981,10(4): 307-337. 2 LIU L. Precise large deviations for dependent random variables with heavy tails[J]. Statistics and Probability Letters, 2009,79(9):1290-1298. DOI: 10.1016/j.spl.2009.02.001. 3 JOAG-DEV K, PROSCHAN F. Negative association of random variables with applications[J]. The Annals of Statistics,1983,11(1):286-295. DOI: 10.1214/aos/1176346079. 4 LIU L. Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails[J]. Science in China (Ser A): Mathematics,2010,53(6):1421-1434. DOI: 10.1007/s11425-010-4012-9. 5 CHEN Y Q, CHEN A Y, NG, KAI W. The strong law of large numbers for extend negatively dependent random variables[J]. Journal of Applied Probability,2010,47:908-922. DOI:10.1017/S0021900200007257. 6 SHEN A T. Probability inequalities for END sequence and their applications[J]. Journal of Inequalities and Applications, 2011, Article ID 98, 12 pages. DOI: 10.1186/1029-242X-2011-98. 7 WU Y F, GUAN M. Convergence properties of the partial sums for sequences of END random variables[J]. Journal of the Korean Mathematical Society, 2012, 49(6): 1097-1110. DOI: 10.4134/JKMS.2012.49.6.1097. 8 WANG S J, WANG X J. Precise large deviations for random sums of END real-valued random variables with consistent variation[J]. Journal of Mathematical Analysis and Applications, 2013, 402:660-667. DOI: 10.1016/j.jmaa.2013.02.002. 9 IBRAGIMOV I A. Some limit theorem for stationary processes[J]. Theory of Probability and Its Applications, 1962(7):349-382. DOI: 10.1137/1107036. 10 ROBERT M B, DEHLING H. Large deviations for some weakly dependent random process[J]. Statistics and Probability Letters, 1990(9):397-401. DOI:10.1016/0617-7152(90)90031-2 11 LI D L, RAO M B , WANG X C. Complete convergence of moving average process[J]. Statistics and Probability Letters, 1992(14): 111-114. DOI: 10.1016/0167-7152(92)90073-E. 12 CHEN P Y, WANG D C. Convergence rates for probabilities of moderate deviations for moving average process[J]. Acta Mathematica Scientia(Eng Ser), 2008,24(4):611-622. DOI: 10.1007/s10114-007-6062-7. 13 李云霞,李坚高. 由随机过程序列产生的滑动平均过程部分和的弱收敛[J]. 数学学报, 2004,47(5): 873-884. DOI: cnki:issn:0583-1431.0.2004-05-005. LI Y X, LI J G. Weak convergence for partial sums of moving average processes generated by stochastic process[J]. Acta Mathematica Sinica, 2004,47(5):873-884. DOI: cnki:issn:0583-1431.0.2004-05-005. 14 ZHANG L X. Complete convergence of moving average processes under dependence assumptions[J]. Statistics and Probability Letters, 1996,30:165-170. DOI: 10.1016/0167-7152(95)00215-4. 15 CHEN P Y, HU T C, VOLODIN A. Limiting behaviour of moving average processes under φ-mixing assumption[J]. Statistics and Probability Letters, 2009,75:105-111. DOI: 10.1016/j.spl.2008.07.026. 16 吴群英.混合序列的概率极限理论[M].北京:科学出版社,2006. WU Q Y. Probability Limit Theory for Mixing Sequences[M]. Beijing: Sicence Press, 2006. 17 SHEN A T, YAO M, XIAO B Q. Equivalent conditions of complete convergence and complete moment convergence for END random variables[J]. Chinese Annals of Mathematics(Ser B), 2018, 39(1): 83-96. DOI: 10.1007/s11401-018-1053-9. 18 LI P H , LI X Q, WU K H. Complete convergence of randomly weighted END and its application[J]. Journal of Inequalities and Applications, 2017(1):182-197. DOI: 10.1186/s13660-017-1457-1. 19 邱德华,陈平炎. END随机变量序列产生的移动平均过程的收敛性[J]. 数学物理学报(A辑), 2015, 35(4):756-768. DOI: 10.3969/j.issn.1003-3998.2015.04.012. QIU D H, CHEN P Y. Convergence for moving average processes under END set-up[J]. Acta Mathematica Scientia(Ser A), 2015,35(4):756-768. DOI: 10.3969/j.issn.1003-3998.2015.04.012. |
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